Geometric Overpass Extraction from Vector Road Data and DSMs Joshua Schpok Google Inc. [email protected] ABSTRACT We present a method to extract elevated road structures, typically overpassing other roads, transit lines, and water- courses. The technique uses a digital surface model (DSM) and roughly aligned vector road data and outputs geome- try approximating the shape and elevation of the elevated road deck. Our method is robust against noise in DSM el- evations and can recover elevated roads partially obscured by trees and other overpasses. We demonstrate our method parallelized over city-wide DSMs, and formulate a confidence metric ranking the fidelity of the reconstruction. Categories and Subject Descriptors I.4.8 [Image Processing and Computer Vision]: Scene Figure 1: Realism is lost without overpass struc- Analysis|Object Recognition; I.4.6 [Image Processing and tures, and it is less clear if these roads intersect. Computer Vision]: Segmentation|Edge and feature de- tection; I.4.7 [Image Processing and Computer Vi- sion]: Feature Measurement|Feature representation of collecting new overpass-specific data. Our method recon- structs overpass structures from 2-meter resolution DSMs 1. INTRODUCTION and aligned vector road paths. Overpass structures are an important part of realistically and accurately representing roadways. Without overpass 2. RELATED WORK structures in a terrain model, roadways in bare digital ter- Several methods have been published to extract overpasses rain models (DTMs) such as in Figure 1 appear unrealistic from geospatial data. Using LIDAR instruments mounted to and do not clearly convey the absence of an intersection be- terrestrial vehicles [7], overpass structures can be detected. tween the crossroads. Though these artifacts may have some This differs from our approach of using a DSM, which has artistic merit [10], they can be visually distracting, difficult wider and more thorough coverage than just those over- to parse visually, and break an immersive experience. passes over drivable, accessible roadways. The shapes of elevated road structures are also useful in the Work extracting elevated roadways solely from panchromatic generation of DTMs, since they are often misclassified [8]. texture [5][4][9] successfully recovers structure over hetero- These structures serve not only as a mask for non-terrain geneous regions, though it fails to identify if two roads of elements, but may also assume roadways not classified as similar constitution cross. elevated are likely on the ground, which can serve as the local terrain elevation [1]. Topographic vector data can be given elevations by fitting them to a LIDAR-derived segmentation [6]. Our datasets With the relative infrequency of overpass structures across lack a complete object segmentation. Though this would terrain, we wish to derive results from existing data instead greatly assist in measuring roads, they are limited in avail- ability over the breadth of terrain we wish to process. In- stead, we measure the road shape as a part of extraction. While this means road geometry may be less accurate, it Permission to make digital or hard copies of all or part of this work for does permit extraction in regions where only road contours personal or classroom use is granted without fee provided that copies are exist. not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to Among other properties, the geometry of elevated road struc- republish, to post on servers or to redistribute to lists, requires prior specific tures can be reconstructed solely from LIDAR and multi- permission and/or a fee. ACM SIGSPATIAL GIS ’11, November 1–4, 2011, Chicago, IL, USA. spectral imagery [3]. The results are tuned for urban en- Copyright c 2011 ACM ISBN 978-1-4503-1031-4/11/11. $10.00 vironments, where stretches of continuous flat terrain are extracted as roads. It is unclear how the algorithm per- forms in windy, hilly roads, and results demonstrate some tracking limitations without vector road data. 3. METHOD Our method can be divided into four sequential steps, out- lined in Figures 2 and 5. First, vector road data is used to measure road spans by finding drop-offs perpendicular to the road direction. Next, road spans are clustered by a distance metric defined in Section 3.2. These clusters are merged to form continuous overpass structures in Section 3.3. Fi- nally, the road spans are rebuilt into a geometric model in Section 3.4. 3.1 Span Measurement For all road segments, we sample a 1-dimensional cross sec- tion perpendicular to the road direction to find a drop-off and determine if this segment could be part of an overpass. We express our surface model as DSM : 2 7! , mapping a R R (a) Sample points in A along road vectors. two-dimensional surface coordinate to its surface elevation. In our implementation, this function bilinearly interpolates a 2-meter grid. We sample a new cross section maximally at every DSM grid cell along a road segment. This sampling rate can be reduced for efficiency at the cost of modeling robustness. Road span quantities are illustrated in Figure 3. We define the elevation cross section originating from a road point x as: f+(t) = DSM(x + nt); 0 < t < bmax (1) f−(t) = DSM(x − nt); 0 < t < bmax (2) where n is a unit direction perpendicular to the road, and bmax is a practical maximum overpass breadth. We ob- serve height discontinuities from the moving average with the function: 1 Z t g(t) = f(t) − f(s) ds: (3) t 0 With j as a user-tunable drop-off threshold, we attempt to (b) Road spans with measured drop-offs M. minimize t for Equations 1 and 2 such that −j > g(t), where t is bounded 0 < t < bmax, and there exists no u < t such that j < g(u), representing a height discontinuity from the rolling average upwards. In addition, this measurement may be rejected early by testing if x lies within a cell classified as vegetation1. This avoid misinterpreting the canopies of tree-lined streets as the deck of an elevated road. Finding a minimal t for f+ and f− gives us values t+ and t−, from which we compute approximate span breadth in grid space: b = t+ + t− (4) a revised road span midpoint: m = x + n (t+ − t−) (5) and elevation: 1 Z t+ h = DSM(x + ns) ds: (6) b −t− 1We classify vegetative cells as having a high normalized (c) Clustered and extended road spans C. difference vegetation index (NDVI), computed from existing aerial imagery. Figure 2: Stages of road span processing. Figure 3: Road span quantities. A point x along a road vector (dashed, yellow) has a perpendicular vector n. If drop-offs (solid, gray) are found along x + nt for t+ and t−, breadth b and midpoint m can be computed. Figure 4: Vector roadways are reconstructed from DSM measurements instead of the original vector data because multiple vector thoroughfares may be These measurements are attempted for all road spans A, sharing the same structure. Here, vehicular (yel- constructing a subset of spans M where t+ and t− are suc- low) and pedestrian (red) traffic disjointly share the cessfully found. Colorado Boulevard Bridge in Pasadena, California. 3.2 Span Clustering The next step is to divide the set of measured road spans M 3.3 Overpass Growing into subsets C where the spans form a continuous length. We After clustering measured road spans, we grow each subset achieve this with single-linkage clustering: Beginning with C to include certain road spans from outgoing edges. From an outgoing edge fcγ ; ag cγ 2 Cγ ; a 2 A n Cγ , a road span a every road span in its own set, sets Cφ and Cθ are merged if the minimum distance between any two elements of either is added to Cγ if its direction is similar by Equation 10, and set is less than 1: the path along the vertices Cγ to the nearest member of M is within a growth threshold, qg. This criterion can be ex- minfd(cφ; cθ): cφ 2 Cφ; cθ 2 Cθg < 1 (7) pressed as single-linkage clustering using a distance function of: Our distance metric measures difference in position, direc- tion, and breadth from the terms of Section 3.1: dgrow(cγ ; a) =max fdm; dgg (12) dg =minfw(Cγ ; a; cm): cm 2 M \ Cγ g=qg (13) dcluster(φ, θ) = max fdm; dn; dbg (8) dm = qm mφ − mθ (9) where w is graph length using the Euclidean distance of source points x between directly-connected vertices. We dn = qn j1 − nφ · nθj (10) consider road span a a continuation of Cγ and add it to db = qb (bφ − bθ) (11) that set when dgrow < 1. The q scalars adjust the sensitivity of each of these compo- As per single-linkage clustering, if a candidate span a be- longs to another cluster Cβ , sets Cγ and Cβ are merged. nents. Ideally qn is small enough to avoid clustering with intersecting roads heading other directions, yet large enough The scalar qg adjusts how far overpass segments will grow, not only to connect broken regions of a common overpass to follow the road as it curves. Similarly, qb is small enough to avoid merging ramps with wide freeway decks, yet large structure, but to extend these structures into berms. This enough to accommodate some minor width fluctuation. is a useful result to connect overpasses into terrain where a clear drop-off will not be observed. We formulate the distance Equation 8 without road network connectivity to combine disjoint roadways sharing a common 3.4 Geometric Reconstruction overpass structure.